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Physical Review A

Controlled- X gate with cache function for one-way quantum computation

Heng Shen, Kenan Qu, Weigang Zhang, Jing Jin

Published Mar 16, 2012• 3 citations
Publisher

Abstract

One-way quantum computation by utilizing multipartite cluster states paves the way for the realization of universal quantum computation. However, quantum memory should be implemented in the practical systems to ensure the operations could be timed appropriately. A scheme of the controlled-$X$ gate with a cache function for one-way quantum computation is proposed here. Due to the generation of a hybrid cluster state based on the interaction of light-atoms, the atom stations will not only be treated as the submodes of cluster states, but also implement the function of quantum memory.

DOI
10.1103/physreva.85.032317

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One-way quantum computation by utilizing multipartite cluster states paves the way for the realization of universal quantum computation. However, quantum memory should be implemented in the practical systems to ensure the operations could be timed appropriately. A scheme of the controlled-XXX gate with a cache function for one-way quantum computation is proposed here. Due to the generation of a hybrid cluster state based on the interaction of light-atoms, the atom stations will not only be treated as the submodes of cluster states, but also implement the function of quantum memory.
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the cluster state needed for the computation and its consumption by measurements are carried out simultaneously. As a consequence, effective clusters of one spatial dimension fewer than in the standard approach are sufficient for computation. In particular, universal computation requires only a one-dimensional array of memories. The scheme applies to discrete-variable systems of any dimension as well as to continuous-variable ones, and both are treated equivalently under the light of local complementation of graphs. In this way our formalism introduces a general framework that encompasses and generalizes in a unified manner some previous system-dependent proposals. The procedure is intrinsically well suited for implementations with atom-photon interfaces.
For realizing a quantum memory the encoded quantum information can be protected against decoherence via repeated decoding and re-encoding operations. This requires us to perform fast encoding and decoding operations. The computational model underlying the one-way quantum computer provides a suitable concept for a fast implementation, which has been solved in a previous article for the encoding operation. In the present paper we show that the missing part, the decoding operation, can also be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.
We describe the application of four-qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic operations of one-way quantum computation. These consist of arbitrary single-qubit rotations, either probabilistic or deterministic, and simple two-qubit gates, such as a controlled-NOT (CNOT) gate for equatorial qubits and a universal controlled-phase gate (controlled-ZZZ or CZ) gate acting on arbitrary target qubits. Other basic computation operations, such as the Grover's search and the Deutsch's algorithms, have been realized by using these states. In all the cases we obtained a high value of the operation fidelities. These results demonstrate that cluster states of two photons entangled in many degrees of freedom are good candidates for the realization of more complex quantum computation operations based on a larger number of qubits.
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantum computer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding and decoding operations for stabilizer codes can be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.
One-way quantum computation is a promising scheme for realizing large-scale quantum computation, where computation is done via measurements on a universal multi-mode entangled resource called cluster state. The capability of this method is determined by the size and the dimension of the cluster state; the size is roughly equivalent to the number of input modes times number of operation steps, while the dimension determines universality and fault tolerance of the computation. To achieve universality, two-dimensional cluster state is required. Among many approaches, time-domain multiplexing using optical system [1, 2] is a promising method where quantum state is encoded in a temporal wave packet. Although universality is still lacking, one-million-mode one-dimensional cluster state has been demonstrated with this approach [3].
Measurement-based one-way quantum computation using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian quantum computation can be implemented sufficiently by long single-mode and two-mode gate sequences. However, continuous variable gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first continuous variable gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian quantum computation by means of accessible gate sequences. Measurement-based one-way quantum computation with cluster states is an efficient route to processing quantum information, yet gate sequences for large states remain elusive. Su et al. present a continuous variable squeezed gate and controlled-phase gate sequence using a six-mode cluster state.